Where was the FDR sent for data read-out? I would assume it went back to the American manufacturer, and if it's the FDR's manufacturer saying it's unreadable, that might be taken as reliable information.
A double flame-out is no joke; if there's some problem with this series of aircraft then the industry really needs to see those data. As is, I suppose everyone else just shrugs and assumes some sort of screw-up that is unique to Nigeria, something down to a lack of operating standards. There certainly have been plenty of accidents caused by that, and that situation probably persists despite all the fancy rhetoric about FAA approval and what-not.
Abuja-Lagos is a fairly short sector so that it's hard to imagine an accident caused by running out of fuel, but that is the most common cause for a dual engine failure! A dual bird-strike (at five thousand feet?), synchronous catastrophic mechanical failures in both engines, some way the power levers ('throttles') came disconnected from both engines, fuel contamination... all of these seem like pretty wild guesses, compared to simple fuel starvation.
This would have to be tracked down by looking at some chain of events such as mis-fueling coupled with fuel level indicator problems and a failure to verify the fuel state prior to departure. That's doable, just not as simple as looking at the FDR read-out to see indications of fuel starvation.
It will be interesting to see where the accident investigation goes from the point where we have been told that the FDR is unreadable.